Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | A4×#73105 |
1700 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 1700 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,3,4)(5,8,6)(9,11,13,20,14,21,12,19)(10,15,16,18,17,23,22,24);(1,4)(2,3)(7,8)(9,10,12,16,14,17,13,22)(11,18,19,23,21,24,20,15)176 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3,4)(5,8,6)(9,11,13,20,14,21,12,19)(10,15,16,18,17,23,22,24), (1,4)(2,3)(7,8)(9,10,12,16,14,17,13,22)(11,18,19,23,21,24,20,15));